What Is the Francis Turbine Specific Speed & Sizing Calculator?
Specific speed Ns defines the geometric and kinematic characteristics of a hydraulic turbine independently of physical size.
It dictates whether a Francis runner should have a radial, mixed, or high-discharge axial contour.
How Does the Francis Turbine Specific Speed & Sizing Calculator Work?
Low Ns (<120) corresponds to high-head runners with large diameter D1 and narrow distributor height b1.
High Ns (>250) corresponds to low-head runners with smaller D1 and larger distributor openings.
Francis Turbine Specific Speed & Sizing Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
N_s = \frac{N \sqrt{P}}{H^{5/4}}, \quad Q = \frac{P}{\rho g H \eta}, \quad D_1 = \frac{60 u_1}{\pi N}
Standard metric specific speed definition and empirical Francis runner sizing formulas.
How to Use the Francis Turbine Specific Speed & Sizing Calculator
- Input turbine power, head, rotational speed, and expected efficiency.
- Review metric Ns, discharge flow rate Q, and runner inlet dimensions.
Step-by-Step Example Calculation
30 MW Hydroelectric Unit
Input Values:
powerOutputKW:30000
effectiveHeadMeters:110
rotationalSpeedRpm:500
overallEfficiencyPercent:92
Worked Steps: Determines Francis runner classification and inlet dimensions.
Understanding Your Result
Specific speed indicates runner profile and optimal setting depth.
Factors That Affect the Result
- Higher head decreases specific speed, leading to slower, larger-diameter runners.
When Should You Use This Calculator?
- Preliminary sizing and feasibility studies for hydro power plants.
Assumptions & Limitations
- Uses standard empirical correlations for Francis best efficiency point design.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard USBR / Bovet turbomachinery dimensioning methodology.